Finite Group Databasebeta

← #29583362

Subgroups — #29583362

Order 15616.

620 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 620 conjugacy classes of subgroups — too many to draw. Only its 113 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21451933C211yesmaximal, characteristic
2#21446124C212yesmaximal
3C2×#16839500C212yesmaximal
4#21444083C211yesmaximal, characteristic
5C61×#1280C211yesmaximal, characteristic
6C2×#14519756C2212yes—
7C22×C4⋊Dic61C2211yescharacteristic
8C22×#11758196—21no—
9C2×#14519702—22no—
10#16839694—22no—
11#16839683—22no—
12#16839622—21no—
13#16839622—21no—
14C2×#14519684—21no—
15C2×#14519684C2211yescharacteristic
16#16839525—22no—
17#16839500—24no—
18C2×C22⋊C8×C61C2212yes—
19C2×#95×C61C2211yescharacteristic
20C22×Dic122D412yes—
21C23×Dic61—21no—
22C23×Dic61—21no—
23#14519756—22no—
24#14519756—22no—
25#14519756—22no—
26#14519756—22no—
27C2×C4⋊Dic61—22no—
28C2×C4⋊Dic61—21no—
29C2×C4⋊Dic61—21no—
30C2×C4⋊Dic61—21no—
31C2×C4⋊Dic61—21no—
32C2×C4⋊Dic61—42no—
33C2×C4⋊Dic61D412yes—
34C2×#11758196—22no—
35C2×#11758196—42no—
36C2×#11758196—42no—
37C2×#11758196—42no—
38C2×C22⋊Dic61—22no—
39#14519702—44no—
40#14519684—22no—
41#14519684—22no—
42#14519684—21no—
43#14519684—42no—
44#14519684D412yes—
45C23×C4×C61D411yescharacteristic
46C23×C4×C61D411yescharacteristic
47C23×C4×C61C2311yescharacteristic
48C22×C8×C61—22no—
49C22⋊C8×C61—22no—
50C22⋊C8×C61—22no—
51#95×C61—22no—
52C24×C61C2×D411yescharacteristic
53C22×C4×C61—21no—
54C22×C4×C61—21no—
55C22×C4×C61—21no—
56C22×C4×C61—21no—
57C22×C4×C61—41no—
58C22×C4×C61—41no—
59C22×C4×C61—41no—
60C22×C4×C61—41no—
61C22×C4×C61—41no—
62C22×C4×C61—41no—
63C22×C4×C61SD1612yes—
64C22×C4×C61Q1612yes—
65C22×C4×C61C2×D412yes—
66C22×C4×C61C2×D411yescharacteristic
67C22×C4×C61#4112yes—
68C22×C4×C61#4111yescharacteristic
69C22×Dic61—22no—
70C22×Dic61—22no—
71C22×Dic61—22no—
72C22×Dic61—22no—
73C22×Dic61—22no—
74C22×Dic61—22no—
75C22×Dic61—41no—
76C22×Dic61—41no—
77C22×Dic61—41no—
78C22×Dic61—41no—
79C22×Dic61—41no—
80C22×Dic61—41no—
81C22×Dic61—41no—
82C22×Dic61—41no—
83C22×Dic61—41no—
84C22×Dic61—41no—
85C2×Dic122—22no—
86C2×Dic122—22no—
87C2×Dic122—42no—
88C2×Dic122—42no—
89C2×C8×C61—42no—
90C2×C8×C61—42no—
91C2×C8×C61—42no—
92C22⋊Dic61—42no—
93C22⋊Dic61—42no—
94C4⋊Dic61—24no—
95C4⋊Dic61—22no—
96C4⋊Dic61—22no—
97C4⋊Dic61—42no—
98C4⋊Dic61—81no—
99C4⋊Dic61—81no—
100C4⋊Dic61—81no—
101C4⋊Dic61—81no—
102#11758196—48no—
103#11758196—42no—
104#11758196—42no—
105C23×C61—21no—
106C23×C61—21no—
107C23×C61—21no—
108C23×C61—21no—
109C23×C61#12011yescharacteristic
110C23×C61#12111yescharacteristic
111C23×C61#12411yescharacteristic
112C23×C61C2×SD1611yescharacteristic
113C23×C61C2×Q1611yescharacteristic
114C23×C61#13711yescharacteristic
115C23×C61#13711yescharacteristic
116C2×C4×C61—22no—
117C2×C4×C61—22no—
118C2×C4×C61—22no—
119C2×C4×C61—22no—
120C2×C4×C61—41no—
121C2×C4×C61—42no—
122C2×C4×C61—41no—
123C2×C4×C61—41no—
124C2×C4×C61—41no—
125C2×C4×C61—41no—
126C2×C4×C61—41no—
127C2×C4×C61—42no—
128C2×C4×C61—42no—
129C2×C4×C61—81no—
130C2×C4×C61—81no—
131C2×C4×C61#12112yes—
132C2×C4×C61#12312yes—
133C2×Dic61—24no—
134C2×Dic61—42no—
135C2×Dic61—42no—
136C2×Dic61—42no—
137C2×Dic61—42no—
138C2×Dic61—42no—
139C2×Dic61—42no—
140C2×Dic61—42no—
141C2×Dic61—42no—
142C2×Dic61—42no—
143C2×Dic61—42no—
144C2×Dic61—42no—
145C2×Dic61—42no—
146C2×Dic61—42no—
147C2×Dic61—42no—
148C2×Dic61—42no—
149C2×Dic61—81no—
150C2×Dic61—81no—
151C2×Dic61—81no—
152C2×Dic61—81no—
153Dic122—44no—
154Dic122—82no—
155C8×C61—82no—
156#10406—611nomaximal, Sylow
157C22×C61—21no—
158C22×C61—21no—
159C22×C61—21no—
160C22×C61—21no—
161C22×C61—21no—
162C22×C61—21no—
163C22×C61—21no—
164C22×C61—21no—
165C22×C61—21no—
166C22×C61—21no—
167C22×C61—21no—
168C22×C61—21no—
169C22×C61#39411yescharacteristic
170C22×C61#44811yescharacteristic
171C22×C61#45111yescharacteristic
172C22×C61#45311yescharacteristic
173C22×C61#45611yescharacteristic
174C22×C61B(4,𝔽2)11yescharacteristic
175C22×C61#45811yescharacteristic
176C22×C61#46111yescharacteristic
177C22×C61#46211yescharacteristic
178C22×C61#48711yescharacteristic
179C22×C61#49111yescharacteristic
180C4×C61—22no—
181C4×C61—22no—
182C4×C61—42no—
183C4×C61—42no—
184Dic61—44no—
185Dic61—82no—
186Dic61—82no—
187Dic61—82no—
188#2659—611no—
189#1872—612no—
190C2×#328—612no—
191#1444—611no—
192#1280D6111yescharacteristic
193C2×C61—21no—
194C2×C61—21no—
195C2×C61—21no—
196C2×C61—21no—
197C2×C61#159611yescharacteristic
198C2×C61#160511yescharacteristic
199C2×C61#161111yescharacteristic
200C2×C61#161411yescharacteristic
201C2×C61#203911yescharacteristic
202C2×C61#204311yescharacteristic
203C2×C61#204411yescharacteristic
204C2×C22⋊Q8—612no—
205C22×C4⋊C4—611no—
206C22×C4⋊C4—1221no—
207C2×#103—1222no—
208C2×C22⋊C8C2×D6112yes—
209#398—1222no—
210#395—1222no—
211#380—1221no—
212#380—1221no—
213C2×#95—611no—
214C2×#95—1221no—
215C2×#95C2×D6111yescharacteristic
216#340—1222no—
217#328—1224no—
218C61#1040611yescharacteristic, complemented, Sylow
219C22×Q8—612no—
220C23×C4—1221no—
221C23×C4—1221no—
222C23×C4D24411yescharacteristic
223C23×C4D24411yescharacteristic
224C23×C4C22×D6111yescharacteristic
225C22×C8—22no—
226C22⋊Q8—1222no—
227C22⋊Q8—1222no—
228C22⋊Q8—1222no—
229C22⋊Q8—1222no—
230C2×C4⋊C4—612no—
231C2×C4⋊C4—1222no—
232C2×C4⋊C4—1221no—
233C2×C4⋊C4—1221no—
234C2×C4⋊C4—1221no—
235C2×C4⋊C4—1221no—
236C2×C4⋊C4—1222no—
237C2×C4⋊C4—2442no—
238C2×C4⋊C4—2442no—
239C2×C4⋊C4—2442no—
240C2×C4⋊C4—2442no—
241C2×C22⋊C4—1222no—
242#103—2444no—
243C22⋊C8—22no—
244C22⋊C8—22no—
245#95—22no—
246#95—612no—
247#95—1222no—
248#95—1222no—
249#95—1221no—
250#95—2442no—
251C24C2×D24411yescharacteristic
252C2×Q8—1222no—
253C2×Q8—1222no—
254C2×Q8—2442no—
255C2×Q8—2442no—
256C22×C4—21no—
257C22×C4—21no—
258C22×C4—21no—
259C22×C4—21no—
260C22×C4—41no—
261C22×C4—41no—
262C22×C4—41no—
263C22×C4—41no—
264C22×C4—41no—
265C22×C4—41no—
266C22×C4—1222no—
267C22×C4—1222no—
268C22×C4—1222no—
269C22×C4—1222no—
270C22×C4—1222no—
271C22×C4—1222no—
272C22×C4—2441no—
273C22×C4—2441no—
274C22×C4—2441no—
275C22×C4—2441no—
276C22×C4—2441no—
277C22×C4—2441no—
278C22×C4—2441no—
279C22×C4—2441no—
280C22×C4—2441no—
281C22×C4—2441no—
282C22×C4#1175819012yes—
283C22×C4Dic24412yes—
284C22×C4#1175822212yes—
285C22×C4D4×D6112yes—
286C22×C4D4×D6111yescharacteristic
287C22×C4#1175822611yescharacteristic
288C2×C8—42no—
289C2×C8—42no—
290C2×C8—42no—
291C4⋊C4—1224no—
292C4⋊C4—1222no—
293C4⋊C4—1222no—
294C4⋊C4—4881no—
295C4⋊C4—4881no—
296C4⋊C4—4881no—
297C4⋊C4—4881no—
298C4⋊C4—2442no—
299C4⋊C4—2448no—
300C4⋊C4—2442no—
301C4⋊C4—2442no—
302C22⋊C4—2442no—
303C22⋊C4—2442no—
304C23—21no—
305C23—21no—
306C23—21no—
307C23—21no—
308C23#1451974711yescharacteristic
309C23#1451975211yescharacteristic
310C23#1451976511yescharacteristic
311C23C2×#1175819011yescharacteristic
312C23C2×Dic24411yescharacteristic
313C23#1451981011yescharacteristic
314C23#1451981011yescharacteristic
315Q8—4882no—
316Q8—2444no—
317C2×C4—22no—
318C2×C4—22no—
319C2×C4—22no—
320C2×C4—22no—
321C2×C4—42no—
322C2×C4—41no—
323C2×C4—41no—
324C2×C4—41no—
325C2×C4—41no—
326C2×C4—41no—
327C2×C4—41no—
328C2×C4—42no—
329C2×C4—42no—
330C2×C4—81no—
331C2×C4—81no—
332C2×C4—1224no—
333C2×C4—4881no—
334C2×C4—4881no—
335C2×C4—4881no—
336C2×C4—4881no—
337C2×C4—2442no—
338C2×C4—2442no—
339C2×C4—2442no—
340C2×C4—2442no—
341C2×C4—2442no—
342C2×C4—2442no—
343C2×C4—2442no—
344C2×C4—2442no—
345C2×C4—2442no—
346C2×C4—2442no—
347C2×C4—2442no—
348C2×C4—2442no—
349C2×C4—2442no—
350C2×C4—2442no—
351C2×C4—2442no—
352C2×C4#1451975012yes—
353C2×C4#1451976212yes—
354C8—82no—
355C22—21no—
356C22—21no—
357C22—21no—
358C22—21no—
359C22—21no—
360C22—21no—
361C22—21no—
362C22—21no—
363C22—21no—
364C22—21no—
365C22—21no—
366C22—21no—
367C22#1683968011yescharacteristic
368C22#1683990311yescharacteristic
369C22#1683992011yescharacteristic
370C22#1683993211yescharacteristic
371C22#1683994711yescharacteristic
372C22#1683995011yescharacteristic
373C22#1683995311yescharacteristic
374C22#1683996811yescharacteristic
375C22#1683997311yescharacteristic
376C22#1684011311yescharacteristic
377C22#1684013111yescharacteristic
378C4—22no—
379C4—22no—
380C4—42no—
381C4—42no—
382C4—4882no—
383C4—4882no—
384C4—4882no—
385C4—2444no—
386C2—21no—
387C2—21no—
388C2—21no—
389C2—21no—
390C2#2144474411yescharacteristic
391C2#2144479511yescharacteristic
392C2#2144482911yescharacteristic
393C2#2144484611yescharacteristic
394C2#2144704411yescharacteristic
395C2#2144706611yescharacteristic
396C2#2144707111yescharacteristic
subgroupG/H
centerC23#14519747
commutator, cosocleC23×C4×C61C23
FrattiniC23×C4C22×D61
FittingC61×#1280C2
socleC23×C61#120
prime radicalC24×C61C2×D4
hypercenter#1280D61
hypocenterC61#10406
LCSG ▷ C23×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1280

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
218. C61#10406semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#214519332
#214461242
C2×#168395002
#214440832
C61×#12802
#1040661